The present invention relates to pumps and more particularly to air-operated diaphragm pumps. Conventional air-operated diaphragm pumps typically include a diaphragm positioned within a diaphragm chamber surrounded by a diaphragm housing. The diaphragm housing is comprised of an air cap and a fluid cap that cooperate to form the diaphragm housing. The diaphragm chamber is comprised of two separate chambers: an air chamber and a fluid chamber. On one side of the diaphragm, between the air cap and the diaphragm, the air chamber is formed. Air is alternatingly supplied and evacuated from the air chamber to drive the diaphragm back and forth. On the other side of the diaphragm, between the diaphragm and the fluid cap, the fluid chamber is formed, through which a fluid to be pumped flows as the diaphragm moves back and forth. In conventional pumps, the air cap and fluid cap are typically formed with inner surfaces of a constant radius or other simple shape. The diaphragm is often coupled to one end of a piston, which may be coupled on its other end to a second diaphragm in a double-diaphragm arrangement.